Multilevel first-order system least squares for elliptic grid generation

A. L. Codd; T. A. Manteuffel; S. F. Mccormick; J. W. Ruge

doi:10.1137/S0036142902404418

Multilevel first-order system least squares for elliptic grid generation

A. L. Codd^*, T. A. Manteuffel, S. F. Mccormick, J. W. Ruge

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

A new fully variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [A. L. Codd, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 41 (2003), pp. 2197-2209] that involves using Newton's method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equation. The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. The present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments.

Original language	English
Pages (from-to)	2210-2232
Number of pages	23
Journal	SIAM Journal on Numerical Analysis
Volume	41
Issue number	6
DOIs	https://doi.org/10.1137/S0036142902404418
Publication status	Published - 2003

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abstract = "A new fully variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [A. L. Codd, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 41 (2003), pp. 2197-2209] that involves using Newton's method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equation. The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. The present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments.",

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T1 - Multilevel first-order system least squares for elliptic grid generation

AU - Codd, A. L.

AU - Manteuffel, T. A.

AU - Mccormick, S. F.

AU - Ruge, J. W.

PY - 2003

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AB - A new fully variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [A. L. Codd, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 41 (2003), pp. 2197-2209] that involves using Newton's method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equation. The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. The present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments.

KW - Least-squares discretization

KW - Multigrid

KW - Nonlinear elliptic boundary value problems

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DO - 10.1137/S0036142902404418

M3 - Article

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EP - 2232

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

Multilevel first-order system least squares for elliptic grid generation

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